What is the integral from pi/3 to pi/2 of csc^2(x) ?

The integral from pi/3 to pi/2 of csc^2(x) is 1/(sqrt(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from pi/3 to pi/2 of csc^2(x)

\int_{\frac{π}{3}}^{\frac{π}{2}} csc^{2} (x) d x

\frac{1}{3}

Decimal Notation

0.57735 \dots

Solution steps

\int_{\frac{π}{3}}^{\frac{π}{2}} csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= [- cot (x)]_{\frac{π}{3}}^{\frac{π}{2}}

Compute the boundaries:

\frac{1}{3}

= \frac{1}{3}

\int_{0}^{1} \frac{1}{x 4 - x ^{2}} d x

\int_{2}^{3} \frac{1}{x ^{2}} - x d x

\int_{0}^{4} 2 x (x^{2} + 4)^{2} d x

\int_{0}^{3} \frac{1}{16 + x ^{2}} d x

\int_{- 1}^{0} (6 x) d x

What is the integral from pi/3 to pi/2 of csc^2(x) ?
The integral from pi/3 to pi/2 of csc^2(x) is 1/(sqrt(3))